Mutations are straight buffs to certain aspects of a caste or hive. Each Xeno has mutators they can purchase for themselves, while the Queen also has the ability to obtain Mutators that affect the entire hive and those under her.
With each Maturation (Young | Mature | Elder | Ancient) you will gain 3 points to spend on a mutation of your choice. When you evolve you will lose all the mutators you previously picked. Each Xeno can purchase all Positive Mutations available to their caste once, while Keystone mutators are mutually exclusive - you can only ever buy one.
Under the Alien tab you can buy mutations for yourself with the Purchase Mutators verb. To buy mutations for the hive (as the Queen) click on the verb Purchase Hive Mutators. To view the Hive and your own currently active mutations click on the List Mutators verb.